For the following quadratic equation, find the discriminant.
4, x, squared, minus, 45, x, minus, 269, equals, 7, x, squared, minus, 3, x, plus, 7
4x
2
−45x−269=
7x
2
−3x+7
To find the discriminant of the quadratic equation, we need to rewrite it in the standard form: ax^2 + bx + c = 0.
The original equation is:
4x^2 - 45x - 269 = 7x^2 - 3x + 7
Rearranging terms:
7x^2 - 4x^2 - 45x + 3x - 269 - 7 = 0
Simplifying:
3x^2 - 42x - 276 = 0
Now we can identify the coefficients:
a = 3, b = -42, c = -276
The discriminant is calculated using the formula: D = b^2 - 4ac
Plugging in the values we have:
D = (-42)^2 - 4(3)(-276)
D = 1764 + 3312
D = 5076
Therefore, the discriminant of the equation is 5076.